Genes are parts of the genome which encode for proteins in an organism. Proteins play an important part in many biologicl processes in any organism. Measuring expression level of a gene helps biologists estimate the amount of protein produced by that gene. Microarrays can be used to measure the expression levels of thousands of genes in a single experiment. Using additional techniques such as clustering various correlations among genes of interest can be found. The most commonly used clustering technique for microarray data analysis is hierarchical clustering. Various metrics such ad Euclidean, Manhattan, Pearson correlation coefficient have been used to measure (dis)similarity between genes. A commonly used software for hierarchical clustering based on Pearson correlation coefficient takes O(N[Arrow pointing up]3) for clustering N genes, even though there are algorithms which can reduce the runtime to O(N[Arrow pointing up]2). In this thesis, we show how the runtime can be reduced to O(N log N) by using a geometric interpretation of the Pearson correlation coeffcient and show that it is optimal.